Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ab8k)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.ab8k.01

Input Form

HypergeometricPFQ[{-(1/4)}, {-(1/2), 19/4}, z] == (1/(536870912 z^(15/4))) ((1155 (4 z^(1/4) (2297295 + 3063060 Sqrt[z] + 1664208 z + 351936 z^(3/2) - 8960 z^2 + 23552 z^(5/2) - 4096 z^3 + 16384 z^(7/2) + E^(4 Sqrt[z]) (-2297295 + 3063060 Sqrt[z] - 1664208 z + 351936 z^(3/2) + 8960 z^2 + 23552 z^(5/2) + 4096 z^3 + 16384 z^(7/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-2297295 + 786240 z - 207360 z^2 + 81920 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-2297295 + 786240 z - 207360 z^2 + 81920 z^3 + 65536 z^4) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]